# How can I initialize a state with chosen amplitudes in Qiskit?

I was trying to initialize to an arbitrary state of n qubits with the initialize() from Qiskit but it doesn't generate a state with the same amplitudes passed as an argument, instead, it creates a state that when compared to the wanted state will have fidelity equals $$1$$. (described here)

My question is: Is there any method that can generate a state that will have numerically same wanted amplitudes ?

Edit: Just found the PrepareArbitraryState in Q# that does the same thing, they are based in the same paper but some results seen different between then. If someone could explain me the technical differences between then it will be perfect.

Edit(2): Here is the test cited in the Qiskit tutorial:

$$\left|\psi\right\rangle = \frac{i}{4}\left|000\right\rangle + \frac{1}{\sqrt{8}}\left|001\right\rangle + \frac{1+i}{4}\left|010\right\rangle + \frac{1+2i}{\sqrt{8}}\left|101\right\rangle + \frac{1}{4}\left|110\right\rangle$$

Applied to Q# (this result is the same as input and is what I want):

|0⟩     5.970914908063292E-17 + 0.25000000000000017𝑖
|1⟩     0.3535533905932739 + 3.251767952832691E-17𝑖
|2⟩     0.2500000000000002 + 0.25000000000000017𝑖
|3⟩     -2.4061305817955694E-17 + -4.7860913024955035E-18𝑖
|4⟩     -4.845288669732255E-17 + 1.506300336842906E-16𝑖
|5⟩     0.3535533905932743 + 0.7071067811865478𝑖
|6⟩     0.2500000000000002 + -7.897235558417238E-17𝑖
|7⟩     4.7022165029227935E-18 + -4.194489669218219E-17𝑖


Applied to Qiskit (same as the cited tutorial, have fidelity(input, output) = 1, but it doesn't match with the Q# result and it is not what I want):

|0⟩     2.50000000e-01 + 0.j
|1⟩     2.77555756e-17 - 0.35355339j,
|2⟩     2.50000000e-01 - 0.25j
|3⟩     0.00000000e+00 + 0.j
|4⟩     0.00000000e+00 + 0.j
|5⟩     7.07106781e-01 - 0.35355339j
|6⟩     5.89805982e-17 - 0.25j
|7⟩     0.00000000e+00 + 0.j

• You might want to list the results you see as different between them. I don't expect a lot of people are going to be closely familiar with the implementations of both methods, so the more details you provide about your doubts, the higher is your chance of getting a good answer. Jun 7, 2020 at 19:39
• Added. thanks for the feedback :) Jun 7, 2020 at 23:39
• If the state you want and the state you produce have fidelity 1, that means that they do have the same amplitudes, up to a common phase factor $e^{i\gamma}$. Since this is a global phase, it has no observable consequences. Jun 8, 2020 at 6:45